# A rectangular picture measuring 3 in. by 5 in. is surrounded by a frame with uniform width x. How do you write a quadratic function in standard form to show the combined area of the picture and frame?

Jun 9, 2018

$y = 4 {x}^{2} + 16 x + 15$

#### Explanation:

Look at the diagram

The outer length is $= 5 + 2 x$
The outer width is $= 3 + 2 x$

Let the area be $= y$

Then-

$y = \left(5 + 2 x\right) \left(3 + 2 x\right)$

$y = 15 + 6 x + 10 x + 4 {x}^{2}$

$y = 4 {x}^{2} + 16 x + 15$